Fay, Jonathan (2023) On the Relativity of Magnitudes: Delboeuf's forgotten contribution to the 19th Century problem of space. [Preprint]

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Abstract

Faced with the mathematical possibility of non-Euclidean geometries, 19th Century geometers were tasked with the problem of determining which among the possible geometries corresponds to that of our space. In this context, the contribution of the Belgian philosopher-mathematician, Joseph Delboeuf, has been unduly neglected. The aim of this essay is to situate Delboeuf’s ideas within the context of the philosophies of geometry of his contemporaries, such as Helmholtz, Russell and Poincare ́. We elucidate the central thesis, according to which Euclidean geometry is given special status on the basis of the relativity of magnitudes, we uncover its hidden history and show that it is defensible within the context of the philosophies of geometry of the epoch. Through this discussion, we also develop various ideas that have some relevance to present-day methods in gravitational physics and cosmology.

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Item Type:	Preprint
Creators:	Creators Email ORCID Fay, Jonathan hi20625@bristol.ac.uk
Keywords:	Delboeuf Poincare Problem of space Relativity of magnitude, Euclidean Problem of space Relativity of magnitude Euclidean
Subjects:	Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > History Specific Sciences > Physics > Cosmology General Issues > History of Philosophy of Science Specific Sciences > Mathematics General Issues > Models and Idealization Specific Sciences > Physics
Depositing User:	Mr. Jonathan Fay
Date Deposited:	01 Apr 2024 05:39
Last Modified:	01 Apr 2024 05:39
Item ID:	23242
Subjects:	Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > History Specific Sciences > Physics > Cosmology General Issues > History of Philosophy of Science Specific Sciences > Mathematics General Issues > Models and Idealization Specific Sciences > Physics
Date:	24 August 2023
URI:	https://philsci-archive.pitt.edu/id/eprint/23242

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• On the Relativity of Magnitudes: Delboeuf's forgotten contribution to the 19th Century problem of space. (deposited 18 Sep 2023 16:42)

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